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<p>In this study, an artificial neural network (ANN) approach is employed to analyze the thermal and fluid behavior of gold–blood Casson nanofluid flow over a heated stretching sheet, incorporating Joule heating and viscous dissipation. The analysis is based on the advanced Cattaneo–Christov heat flux model, which captures several essential physical effects, including Brownian motion, thermophoresis, chemical reactions, activation energy, Eckert number, Joule heating, and viscous dissipation. The governing nonlinear PDEs are reduced to ODEs via similarity transformations and solved using an intelligent backpropagation neural network with Levenberg–Marquardt optimization in conjunction with the bvp4c solver. A comprehensive dataset was generated by varying critical parameters and partitioned into 80% training, 10% testing, and 10% validation subsets. The ANN model exhibited excellent predictive performance, with regression coefficients approaching unity and mean squared errors ranging from <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(E^{ - 7} {\text{to}}\;E^{ - 3}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>E</mi> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </msup> <mtext>to</mtext> <mspace width="0.277778em" /> <msup> <mi>E</mi> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>. Model reliability was further confirmed through error histograms and fitness curves. Numerical and graphical results were benchmarked against existing literature and showed strong agreement. The findings reveal that fluid velocity decreases under stronger magnetic fields and higher stretching rates, while porous media enhance flow. Thermal transport is significantly improved by Joule heating and viscous dissipation. Furthermore, nanoparticle concentration increases with thermophoresis but diminishes with higher chemical reaction rates.</p>

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Intelligent thermal modeling of gold–blood Casson nanofluid flow via Cattaneo–Christov heat flux and neural network framework

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Naeem Ullah,
  • Wang Jian,
  • Dil Nawaz Khan,
  • Marouan Kouki

摘要

In this study, an artificial neural network (ANN) approach is employed to analyze the thermal and fluid behavior of gold–blood Casson nanofluid flow over a heated stretching sheet, incorporating Joule heating and viscous dissipation. The analysis is based on the advanced Cattaneo–Christov heat flux model, which captures several essential physical effects, including Brownian motion, thermophoresis, chemical reactions, activation energy, Eckert number, Joule heating, and viscous dissipation. The governing nonlinear PDEs are reduced to ODEs via similarity transformations and solved using an intelligent backpropagation neural network with Levenberg–Marquardt optimization in conjunction with the bvp4c solver. A comprehensive dataset was generated by varying critical parameters and partitioned into 80% training, 10% testing, and 10% validation subsets. The ANN model exhibited excellent predictive performance, with regression coefficients approaching unity and mean squared errors ranging from \(E^{ - 7} {\text{to}}\;E^{ - 3}\) E - 7 to E - 3 . Model reliability was further confirmed through error histograms and fitness curves. Numerical and graphical results were benchmarked against existing literature and showed strong agreement. The findings reveal that fluid velocity decreases under stronger magnetic fields and higher stretching rates, while porous media enhance flow. Thermal transport is significantly improved by Joule heating and viscous dissipation. Furthermore, nanoparticle concentration increases with thermophoresis but diminishes with higher chemical reaction rates.